Z₃ Symmetry in the Neutrino Sector: Prediction of the Lightest Neutrino Mass and CP Phase Connection

In [1], Koide's relation Q=(m_e+m_μ+m_τ)/(√m_e+√m_μ+√m_τ)²=2/3 was derived as a consequence of the Z₃ symmetry of the chiral coupling operator with normalization condition |b|/a=1/√2. In the present work we investigate whether this symmetry extends to the neutrino sector. We prove that Q=2/3 is INCOMPATIBLE with observed neutrino masses in both orderings: in normal ordering (m₁<m₂<m₃), the maximum achievable value is Q_max=0.5829<2/3; in inverted ordering, the unique Q=2/3 solution predicts m₁=1644 meV with Σmᵢ=1702 meV, excluded by the cosmological bound Σmᵢ<120 meV. We show that the Z₃ circulant parametrization √mᵢ=A(1+√2·cos(θ+2πi/3)) DOES apply to neutrinos, with parameters A_ν=3.125 meV^½ and θ_ν=147.7°, predicting m₁=0.371 meV (Q_ν=0.522). This prediction is falsifiable by PROJECT 8 (~2032) and future CMB surveys (CMB-S4). We analyze the connection between the Koide angle θ_ν and the CP violation phase in neutrinos δ_CP: θ_ν+θ₂₃=195.3°≈δ_CP=195° (PDG). We discuss why the Z₃ symmetry works for charged leptons but gives Q≠2/3 for neutrinos, and what this implies for the flavor problem.